MathDB

1

Part of 2022 Kosovo & Albania Mathematical Olympiad

Problems(2)

Easy algebra question

Source: KAMO 2022 Grade 9 P1

7/5/2022
If (2x−4x)+(2−x−4−x)=3(2^x - 4^x) + (2^{-x} - 4^{-x}) = 3, find the numerical value of the expression (8x+3⋅2x)+(8−x+3⋅2−x).(8^x + 3\cdot 2^x) + (8^{-x} + 3\cdot 2^{-x}).
algebra
Easy diophantine equation

Source: KAMO 2022 Grades 7-8 P1

7/5/2022
Find all pairs of integers (m,n)(m, n) such that m+n=3(mn+10).m+n = 3(mn+10).
number theoryDiophantine equation